I just test-rode John’s bike. It’s got figure-of-eight handlebars, with the brakes and gears on the near part of them. I was keen to see how they felt to ride on.
Result: the far side (front) of the bars were quite pleasant to ride on, and it was a good ride on the uphill. But the near side of the bars were incredibly close, and riding on them was less fun. In fact, braking on the downhill was rather scary: the arms were so vertical it was a little challenging to hold my weight back. And pushing the weight backwards in the normal way by sticking the bum out wasn’t so easy.
OK, so the bike isn’t my size (I had to raise the saddle a couple of inches, but left the bars in place). Even so, I think I’ve answered my question: I don’t want bars that put the brake levers so close to the body.
 That is, his ‘normal’ bike – he’s also got a shiny new brompton from work.